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RANDOM ORDINARY DIFFERENTIAL EQUATIONS.
Technical rept. Sep 67-Jun 68,
CALIFORNIA UNIV BERKELEY DEPT OF MATHEMATICS
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Existence and uniqueness theorems are proved for solutions in the mean of the random differential equation x ft,x,omega. This is accomplished by determining when a sample path solution is also a solution in the mean. The usual definition of mean stability is generalized to a more useful form. Theorems are developed which relate this general type stability to the stability of the average problem. Finally theorems relating almost sure stability with the stability of the average problem are proved. Author
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